标题： 德西特测地线 显示英文标题

标题： de Sitter geodesics

摘要： 在$(1+3)$维的德西特时空中的测地线被考虑，研究它们的参数如何由共形欧几里得、弗里德曼-勒梅特-罗伯逊-沃尔克、德西特-帕莱夫和静态局部坐标系中与笛卡尔空间坐标相关的守恒量确定。 此外，表明存在一种特殊的静态坐标系，在其中测地线是真正的双曲线，其渐近线由守恒动量和相关对偶动量给出。 显示英文摘要

摘要： The geodesics on the $(1+3)$-dimensional de Sitter spacetime are considered studying how their parameters are determined by the conserved quantities in the conformal Euclidean, Friedmann-Lema\^itre-Robertson-Walker, de Sitter-Painlev\'e and static local charts with Cartesian space coordinates. Moreover, it is shown that there exist a special static chart in which the geodesics are genuine hyperbolas whose asymptotes are given by the conserved momentum and the associated dual momentum.